Homogeneous Solutions for the Biharmonic Problem

Author(s):  
Sergey A. Lurie ◽  
Valery V. Vasiliev

Author(s):  
Xiaojuan Tian ◽  
Yueting Zhou ◽  
Lihua Wang ◽  
Shenghu Ding

AbstractThe contact problem for thermoelectric materials with functionally graded properties is considered. The material properties, such as the electric conductivity, the thermal conductivity, the shear modulus, and the thermal expansion coefficient, vary in an exponential function. Using the Fourier transform technique, the electro-thermo-elastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density, the normal energy flux, and the contact pressure. Meanwhile, the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula. After addressing the non-linearity excited by thermoelectric effects, the particular solutions of the displacement fields can be assessed. The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented. The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials (FGTEMs).



2014 ◽  
Vol 32 (2) ◽  
pp. 83 ◽  
Author(s):  
Mohammed Massar ◽  
EL Miloud Hssini ◽  
Najib Tsouli

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.



Author(s):  
J. Solà-Morales ◽  
M. València

SynopsisThe semilinear damped wave equationssubject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.



2014 ◽  
Vol 270 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Hatem Hajlaoui ◽  
Abdellaziz Harrabi ◽  
Dong Ye


1999 ◽  
Author(s):  
Hwan-Sik Yoon ◽  
Gregory Washington

Abstract In this study, a smart aperture antenna of spherical shape is modeled and experimentally verified. The antenna is modeled as a shallow spherical shell with a small hole at the apex for mounting. Starting from five governing equations of the shallow spherical shell, two governing equations are derived in terms of a stress function and the axial deflection using Reissner’s approach. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are considered as distributed pressure loads on the shell surface instead of being applied as boundary conditions like previous studies. This new way of applying the actuation force necessitates solving for the particular solutions in addition to the homogeneous solutions for the governing equations. The amount of deflections is evaluated from the calculated stress function and the axial deflection. In addition to the analytical model, a finite element model is developed to verify the analytical model on the various surface positions of the reflector. Finally, an actual working model of the reflector is built and tested in a zero gravity environment, and the results of the theoretical model are verified by comparing them to the experimental data.



2020 ◽  
Vol 55 (7) ◽  
pp. 1057-1061
Author(s):  
N. B. Rasulova ◽  
M. B. Rasulov


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